What is the solution for y^{''}+25y=cos(5x) ?

The solution for y^{''}+25y=cos(5x) is y=c_{1}cos(5x)+c_{2}sin(5x)+(xsin(5x))/(10)

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y^{''}+25y=cos(5x)

y^{^{''}} + 25 y = cos (5 x)

y = c_{1} cos (5 x) + c_{2} sin (5 x) + \frac{x sin ( 5 x )}{10}

Solution steps

y^{''} (x) + 25 y = cos (5 x)

Solve linear ODE:

y = c_{1} cos (5 x) + c_{2} sin (5 x) + \frac{x sin ( 5 x )}{10}

y = c_{1} cos (5 x) + c_{2} sin (5 x) + \frac{x sin ( 5 x )}{10}

\frac{d}{d x} ((x - 2) (x^{2} + 4))

\int ln (x^{2} + 13 x + 42) d x

\int \frac{x}{9 x ^{2} + 675} d x

\int \frac{e ^{x}}{x} d x

x \to 1 - lim (\frac{3 + x}{x ^{2} - 1})

What is the solution for y^{''}+25y=cos(5x) ?
The solution for y^{''}+25y=cos(5x) is y=c_{1}cos(5x)+c_{2}sin(5x)+(xsin(5x))/(10)